Quaternary group ring codes: Ranks, kernels and self-dual codes

Steven T. Dougherty, Cristina Fernández-Córdoba, Roger Ten-Valls, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study G-codes over the ring Z4, which are codes that are held invariant by the action of an arbitrary group G. We view these codes as ideals in a group ring and we study the rank and kernel of these codes. We use the rank and kernel to study the image of these codes under the Gray map. We study the specific case when the group is the dihedral group and the dicyclic group. Finally, we study quaternary self-dual dihedral and dicyclic codes, tabulating the many good self-dual quaternary codes obtained via these constructions, including the octacode.

Original languageEnglish (US)
Pages (from-to)319-332
Number of pages14
JournalAdvances in Mathematics of Communications
Issue number2
StatePublished - 2020
Externally publishedYes


  • Dicyclic
  • Dihedral
  • Group ring codes
  • Kernel
  • Quaternary codes
  • Rank
  • Self-dual Codes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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